{"id":3632,"date":"2025-05-03T19:21:49","date_gmt":"2025-05-03T16:21:49","guid":{"rendered":"https:\/\/www.dztecs.com\/ai\/?p=3632"},"modified":"2025-06-13T08:50:17","modified_gmt":"2025-06-13T05:50:17","slug":"when-physics-meets-finance-using-ai-to-solve-black-scholes","status":"publish","type":"post","link":"https:\/\/www.dztecs.com\/ai\/when-physics-meets-finance-using-ai-to-solve-black-scholes\/","title":{"rendered":"\u0639\u0646\u062f\u0645\u0627 \u064a\u0644\u062a\u0642\u064a \u0639\u0644\u0645 \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621 \u0628\u0627\u0644\u062a\u0645\u0648\u064a\u0644: \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0630\u0643\u0627\u0621 \u0627\u0644\u0627\u0635\u0637\u0646\u0627\u0639\u064a \u0644\u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0629 \u0628\u0644\u0627\u0643-\u0634\u0648\u0644\u0632","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"<blockquote><p><strong><em>\u0625\u062e\u0644\u0627\u0621 \u0645\u0633\u0624\u0648\u0644\u064a\u0629<\/em><\/strong>: \u0647\u0630\u0647 \u0644\u064a\u0633\u062a \u0646\u0635\u064a\u062d\u0629 \u0645\u0627\u0644\u064a\u0629. \u0623\u0646\u0627 \u062d\u0627\u0635\u0644 \u0639\u0644\u0649 \u062f\u0631\u062c\u0629 \u0627\u0644\u062f\u0643\u062a\u0648\u0631\u0627\u0647 \u0641\u064a \u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u0637\u064a\u0631\u0627\u0646 \u0645\u0639 \u062a\u0631\u0643\u064a\u0632 \u0642\u0648\u064a \u0639\u0644\u0649 \u062a\u0639\u0644\u0645 \u0627\u0644\u0622\u0644\u0629: \u0623\u0646\u0627 <strong>\u0644\u0633\u062a<\/strong> \u0645\u0633\u062a\u0634\u0627\u0631\u064b\u0627 \u0645\u0627\u0644\u064a\u064b\u0627. \u0647\u0630\u0647 \u0627\u0644\u0645\u0642\u0627\u0644\u0629 \u0645\u062e\u0635\u0635\u0629 \u0641\u0642\u0637 \u0644\u0625\u0638\u0647\u0627\u0631 \u0642\u0648\u0629 \u0627\u0644\u0634\u0628\u0643\u0627\u062a \u0627\u0644\u0639\u0635\u0628\u064a\u0629 \u0627\u0644\u0645\u0633\u062a\u0646\u064a\u0631\u0629 \u0628\u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621 (PINNs) \u0641\u064a \u0633\u064a\u0627\u0642 \u0645\u0627\u0644\u064a.<\/p><\/blockquote>\n<p class=\"wp-block-paragraph\">\u0639\u0646\u062f\u0645\u0627 \u0643\u0627\u0646 \u0639\u0645\u0631\u064a 16 \u0639\u0627\u0645\u064b\u0627\u060c \u0648\u0642\u0639\u062a \u0641\u064a \u062d\u0628 \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621. \u0643\u0627\u0646 \u0627\u0644\u0633\u0628\u0628 \u0628\u0633\u064a\u0637\u064b\u0627 \u0648\u0644\u0643\u0646\u0647 \u0642\u0648\u064a: \u0627\u0639\u062a\u0642\u062f\u062a \u0623\u0646 \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621 <strong><em>\u0639\u0627\u062f\u0644\u0629<\/em><\/strong>.<\/p>\n<p id=\"e^x\" class=\"wp-block-paragraph\">\u0644\u0645 \u064a\u062d\u062f\u062b \u0623\u0628\u062f\u064b\u0627 \u0623\u0646 \u0623\u062e\u0637\u0623\u062a \u0641\u064a \u062a\u0645\u0631\u064a\u0646 \u0644\u0623\u0646 \u0633\u0631\u0639\u0629 \u0627\u0644\u0636\u0648\u0621 \u062a\u063a\u064a\u0631\u062a \u0628\u064a\u0646 \u0639\u0634\u064a\u0629 \u0648\u0636\u062d\u0627\u0647\u0627\u060c \u0623\u0648 \u0644\u0623\u0646\u0647 \u0641\u062c\u0623\u0629 \u064a\u0645\u0643\u0646 \u0623\u0646 \u062a\u0643\u0648\u0646 e<sup>x<\/sup> \u0633\u0627\u0644\u0628\u0629. \u0641\u064a \u0643\u0644 \u0645\u0631\u0629 \u0642\u0631\u0623\u062a \u0641\u064a\u0647\u0627 \u0648\u0631\u0642\u0629 \u0641\u064a\u0632\u064a\u0627\u0626\u064a\u0629 \u0648\u0641\u0643\u0631\u062a\u060c <em>&#8220;\u0647\u0630\u0627 \u0644\u0627 \u064a\u0628\u062f\u0648 \u0645\u0646\u0637\u0642\u064a\u064b\u0627\u060c&#8221;<\/em> \u0627\u062a\u0636\u062d \u0623\u0646 <strong><em>\u0623\u0646\u0627 \u0645\u0646 \u0644\u0645 \u064a\u0643\u0646 \u064a\u0641\u0647\u0645.<\/em><\/strong><\/p>\n<p class=\"wp-block-paragraph\">\u0625\u0630\u064b\u0627\u060c \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621 \u0639\u0627\u062f\u0644\u0629 \u062f\u0627\u0626\u0645\u064b\u0627\u060c \u0648\u0644\u0647\u0630\u0627 \u0627\u0644\u0633\u0628\u0628 \u0641\u0647\u064a \u062f\u0627\u0626\u0645\u064b\u0627 <strong><em>\u0645\u062b\u0627\u0644\u064a\u0629<\/em><\/strong>. \u0648\u062a\u0639\u0631\u0636 \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621 \u0647\u0630\u0627 \u0627\u0644\u0643\u0645\u0627\u0644 \u0648\u0627\u0644\u0639\u062f\u0627\u0644\u0629 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0645\u062c\u0645\u0648\u0639\u0629 \u0627\u0644\u0642\u0648\u0627\u0639\u062f \u0627\u0644\u062e\u0627\u0635\u0629 \u0628\u0647\u0627\u060c \u0648\u0627\u0644\u062a\u064a \u062a\u064f\u0639\u0631\u0641 \u0628\u0627\u0633\u0645 <strong>\u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u062a\u0641\u0627\u0636\u0644\u064a\u0629<\/strong>.<\/p>\n<p><img decoding=\"async\" class=\"attachment-post-thumbnail size-post-thumbnail not-transparent wp-post-image aligncenter\" src=\"https:\/\/www.dztecs.com\/ai\/wp-content\/uploads\/sites\/2\/2025\/05\/Post_Pic.png\" alt=\"\" width=\"1536\" height=\"1024\" data-has-transparency=\"false\" data-dominant-color=\"767269\" \/><\/p>\n<p class=\"wp-block-paragraph\">\u0623\u0628\u0633\u0637 \u0645\u0639\u0627\u062f\u0644\u0629 \u062a\u0641\u0627\u0636\u0644\u064a\u0629 \u0623\u0639\u0631\u0641\u0647\u0627 \u0647\u064a \u0647\u0630\u0647:<\/p>\n<p><img decoding=\"async\" class=\"wp-image-601628 aligncenter\" style=\"width: 409px; height: auto;\" src=\"https:\/\/www.dztecs.com\/ai\/wp-content\/uploads\/sites\/2\/2025\/05\/Differential_Equation-1-1024x559-1.png\" alt=\"\" \/ width=\"1024\" height=\"559\"><\/p>\n<p class=\"wp-block-paragraph\">\u0628\u0633\u064a\u0637 \u062c\u062f\u064b\u0627: \u0646\u0628\u062f\u0623 \u0647\u0646\u0627\u060c x<sub>0<\/sub>=0\u060c \u0641\u064a \u0627\u0644\u0648\u0642\u062a t=0\u060c \u062b\u0645 \u0646\u062a\u062d\u0631\u0643 \u0628\u0633\u0631\u0639\u0629 \u062b\u0627\u0628\u062a\u0629 \u0642\u062f\u0631\u0647\u0627 5 \u0645\/\u062b. \u0647\u0630\u0627 \u064a\u0639\u0646\u064a \u0623\u0646\u0647 \u0628\u0639\u062f \u062b\u0627\u0646\u064a\u0629 \u0648\u0627\u062d\u062f\u0629\u060c \u0646\u0643\u0648\u0646 \u0639\u0644\u0649 \u0628\u0639\u062f 5 \u0623\u0645\u062a\u0627\u0631 (\u0623\u0648 \u0623\u0645\u064a\u0627\u0644\u060c \u0625\u0630\u0627 \u0643\u0646\u062a \u062a\u0641\u0636\u0644 \u0630\u0644\u0643) \u0645\u0646 \u0627\u0644\u0623\u0635\u0644\u061b \u0628\u0639\u062f \u062b\u0627\u0646\u064a\u062a\u064a\u0646\u060c \u0646\u0643\u0648\u0646 \u0639\u0644\u0649 \u0628\u0639\u062f 10 \u0623\u0645\u062a\u0627\u0631 \u0645\u0646 \u0627\u0644\u0623\u0635\u0644\u061b \u0628\u0639\u062f 43128 \u062b\u0627\u0646\u064a\u0629&#8230; \u0623\u0639\u062a\u0642\u062f \u0623\u0646\u0643 \u0641\u0647\u0645\u062a.<\/p>\n<p class=\"wp-block-paragraph\">\u0643\u0645\u0627 \u0643\u0646\u0627 \u0646\u0642\u0648\u0644\u060c \u0647\u0630\u0627 \u0645\u0643\u062a\u0648\u0628 \u0639\u0644\u0649 \u0627\u0644\u062d\u062c\u0631: \u0645\u062b\u0627\u0644\u064a\u060c \u0645\u062b\u0627\u0644\u064a\u060c \u0648\u0644\u0627 \u062c\u062f\u0627\u0644 \u0641\u064a\u0647. \u0648\u0645\u0639 \u0630\u0644\u0643\u060c \u062a\u062e\u064a\u0644 \u0647\u0630\u0627 \u0641\u064a \u0627\u0644\u062d\u064a\u0627\u0629 \u0627\u0644\u0648\u0627\u0642\u0639\u064a\u0629. \u062a\u062e\u064a\u0644 \u0623\u0646\u0643 \u0641\u064a \u0646\u0632\u0647\u0629 \u0623\u0648 \u062a\u0642\u0648\u062f \u0627\u0644\u0633\u064a\u0627\u0631\u0629. \u062d\u062a\u0649 \u0625\u0630\u0627 \u0628\u0630\u0644\u062a \u0642\u0635\u0627\u0631\u0649 \u062c\u0647\u062f\u0643 \u0644\u0644\u0630\u0647\u0627\u0628 \u0628\u0633\u0631\u0639\u0629 \u0645\u0633\u062a\u0647\u062f\u0641\u0629\u060c \u0641\u0644\u0646 \u062a\u062a\u0645\u0643\u0646 \u0623\u0628\u062f\u064b\u0627 \u0645\u0646 \u0627\u0644\u062d\u0641\u0627\u0638 \u0639\u0644\u064a\u0647\u0627 \u062b\u0627\u0628\u062a\u0629. \u0633\u0648\u0641 \u064a\u062a\u0633\u0627\u0631\u0639 \u0630\u0647\u0646\u0643 \u0641\u064a \u0623\u062c\u0632\u0627\u0621 \u0645\u0639\u064a\u0646\u0629\u061b \u0631\u0628\u0645\u0627 \u0633\u062a\u0635\u0627\u0628 \u0628\u0627\u0644\u0634\u0631\u0648\u062f \u0627\u0644\u0630\u0647\u0646\u064a\u060c \u0631\u0628\u0645\u0627 \u0633\u062a\u062a\u0648\u0642\u0641 \u0639\u0646\u062f \u0627\u0644\u0623\u0636\u0648\u0627\u0621 \u0627\u0644\u062d\u0645\u0631\u0627\u0621\u060c \u0648\u0639\u0644\u0649 \u0627\u0644\u0623\u0631\u062c\u062d \u0645\u0632\u064a\u062c \u0645\u0645\u0627 \u0633\u0628\u0642. \u0644\u0630\u0644\u0643 \u0631\u0628\u0645\u0627 \u062a\u0643\u0648\u0646 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u062a\u0641\u0627\u0636\u0644\u064a\u0629 \u0627\u0644\u0628\u0633\u064a\u0637\u0629 \u0627\u0644\u062a\u064a \u0630\u0643\u0631\u0646\u0627\u0647\u0627 \u0633\u0627\u0628\u0642\u064b\u0627 \u063a\u064a\u0631 \u0643\u0627\u0641\u064a\u0629. \u0645\u0627 \u064a\u0645\u0643\u0646\u0646\u0627 \u0641\u0639\u0644\u0647 \u0647\u0648 \u0645\u062d\u0627\u0648\u0644\u0629 \u0627\u0644\u062a\u0646\u0628\u0624 \u0628\u0645\u0648\u0642\u0639\u0643 \u0645\u0646 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u062a\u0641\u0627\u0636\u0644\u064a\u0629\u060c <strong><em>\u0648\u0644\u0643\u0646<\/em> \u0628\u0645\u0633\u0627\u0639\u062f\u0629 <a target=\"_blank\" rel=\"noopener noreferrer\" title=\"Artificial Intelligence\" href=\"https:\/\/www.dztecs.com\/ai\/how-to-level-up-your-technical-skills-in-this-ai-era\/\">\u0627\u0644\u0630\u0643\u0627\u0621 \u0627\u0644\u0627\u0635\u0637\u0646\u0627\u0639\u064a<\/a><\/strong>. \u0647\u0630\u0627 \u0627\u0644\u0645\u0641\u0647\u0648\u0645 \u0628\u0627\u0644\u063a \u0627\u0644\u0623\u0647\u0645\u064a\u0629 \u0641\u064a \u0646\u0645\u0630\u062c\u0629 \u0627\u0644\u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u0645\u0639\u0642\u062f\u0629.<\/p>\n<p class=\"wp-block-paragraph\">\u064a\u062a\u0645 \u062a\u0637\u0628\u064a\u0642 \u0647\u0630\u0647 \u0627\u0644\u0641\u0643\u0631\u0629 \u0641\u064a <a target=\"_blank\" rel=\"noopener noreferrer\" href=\"https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0021999118307125\">\u0627\u0644\u0634\u0628\u0643\u0627\u062a \u0627\u0644\u0639\u0635\u0628\u064a\u0629 \u0627\u0644\u0645\u0633\u062a\u0646\u064a\u0631\u0629 \u0628\u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621<\/a> (PINN). \u0633\u0646\u0635\u0641\u0647\u0627 \u0644\u0627\u062d\u0642\u064b\u0627 \u0628\u0627\u0644\u062a\u0641\u0635\u064a\u0644\u060c \u0648\u0644\u0643\u0646 \u0627\u0644\u0641\u0643\u0631\u0629 \u0647\u064a \u0623\u0646\u0646\u0627 \u0646\u062d\u0627\u0648\u0644 \u0645\u0637\u0627\u0628\u0642\u0629 <em>\u0643\u0644 \u0645\u0646<\/em> \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0648\u0645\u0627 \u0646\u0639\u0631\u0641\u0647 \u0645\u0646 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u062a\u0641\u0627\u0636\u0644\u064a\u0629 \u0627\u0644\u062a\u064a \u062a\u0635\u0641 \u0627\u0644\u0638\u0627\u0647\u0631\u0629. \u0647\u0630\u0627 \u064a\u0639\u0646\u064a \u0623\u0646\u0646\u0627 \u0646\u0641\u0631\u0636 \u0639\u0644\u0649 \u062d\u0644\u0646\u0627 \u0623\u0646 \u064a\u0644\u0628\u064a \u0628\u0634\u0643\u0644 \u0639\u0627\u0645 \u0645\u0627 \u0646\u062a\u0648\u0642\u0639\u0647 \u0645\u0646 \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621. \u0623\u0639\u0644\u0645 \u0623\u0646 \u0647\u0630\u0627 \u064a\u0628\u062f\u0648 \u0648\u0643\u0623\u0646\u0647 \u0633\u062d\u0631 \u0623\u0633\u0648\u062f\u060c \u0623\u0639\u062f\u0643 \u0623\u0646\u0647 \u0633\u064a\u0643\u0648\u0646 \u0623\u0643\u062b\u0631 \u0648\u0636\u0648\u062d\u064b\u0627 \u062e\u0644\u0627\u0644 \u0647\u0630\u0627 \u0627\u0644\u0645\u0642\u0627\u0644.<\/p>\n<p class=\"wp-block-paragraph\">\u0627\u0644\u0622\u0646\u060c \u0627\u0644\u0633\u0624\u0627\u0644 \u0627\u0644\u0643\u0628\u064a\u0631:<\/p>\n<p>&nbsp;<\/p>\n<blockquote><p>\u0645\u0627 \u0639\u0644\u0627\u0642\u0629 \u0627\u0644\u062a\u0645\u0648\u064a\u0644 \u0628\u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621 \u0648\u0627\u0644\u0634\u0628\u0643\u0627\u062a \u0627\u0644\u0639\u0635\u0628\u064a\u0629 \u0627\u0644\u0645\u0633\u062a\u0646\u062f\u0629 \u0625\u0644\u0649 \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621\u061f<\/p><\/blockquote>\n<p class=\"wp-block-paragraph\">\u062d\u0633\u0646\u064b\u0627\u060c \u0627\u062a\u0636\u062d \u0623\u0646 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u062a\u0641\u0627\u0636\u0644\u064a\u0629 \u0644\u064a\u0633\u062a \u0645\u0641\u064a\u062f\u0629 \u0641\u0642\u0637 \u0644\u0644\u0645\u0647\u062a\u0645\u064a\u0646 \u0628\u0642\u0648\u0627\u0646\u064a\u0646 \u0627\u0644\u0643\u0648\u0646 \u0627\u0644\u0637\u0628\u064a\u0639\u064a\u060c \u0628\u0644 \u064a\u0645\u0643\u0646 \u0623\u0646 \u062a\u0643\u0648\u0646 \u0645\u0641\u064a\u062f\u0629 \u0623\u064a\u0636\u064b\u0627 \u0641\u064a <strong>\u0627\u0644\u0646\u0645\u0627\u0630\u062c \u0627\u0644\u0645\u0627\u0644\u064a\u0629<\/strong>. \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u064a\u0633\u062a\u062e\u062f\u0645 \u0646\u0645\u0648\u0630\u062c <strong>Black-Scholes<\/strong> \u0645\u0639\u0627\u062f\u0644\u0629 \u062a\u0641\u0627\u0636\u0644\u064a\u0629 \u0644\u062a\u062d\u062f\u064a\u062f \u0633\u0639\u0631 \u062e\u064a\u0627\u0631 \u0627\u0644\u0634\u0631\u0627\u0621\u060c \u0645\u0639 \u0627\u0641\u062a\u0631\u0627\u0636\u0627\u062a \u0635\u0627\u0631\u0645\u0629 \u0645\u0639\u064a\u0646\u0629\u060c \u0644\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 <strong>\u0645\u062d\u0641\u0638\u0629 \u062e\u0627\u0644\u064a\u0629 \u0645\u0646 \u0627\u0644\u0645\u062e\u0627\u0637\u0631<\/strong>.<\/p>\n<p class=\"wp-block-paragraph\">\u0627\u0644\u0647\u062f\u0641 \u0645\u0646 \u0647\u0630\u0647 \u0627\u0644\u0645\u0642\u062f\u0645\u0629 \u0627\u0644\u0645\u0639\u0642\u062f\u0629 \u0644\u0644\u063a\u0627\u064a\u0629 \u0643\u0627\u0646 \u0630\u0627 \u0634\u0642\u064a\u0646:<\/p>\n<ul class=\"wp-block-list\">\n<li class=\"wp-block-list-item\">\u0625\u0631\u0628\u0627\u0643\u0643 \u0642\u0644\u064a\u0644\u064b\u0627\u060c \u062d\u062a\u0649 \u062a\u0633\u062a\u0645\u0631 \u0641\u064a \u0627\u0644\u0642\u0631\u0627\u0621\u0629 \ud83d\ude42<\/li>\n<li class=\"wp-block-list-item\">\u0625\u062b\u0627\u0631\u0629 \u0641\u0636\u0648\u0644\u0643 \u0628\u0645\u0627 \u064a\u0643\u0641\u064a \u0644\u0631\u0624\u064a\u0629 \u0625\u0644\u0649 \u0623\u064a\u0646 \u064a\u062a\u062c\u0647 \u0643\u0644 \u0647\u0630\u0627.<\/li>\n<\/ul>\n<p class=\"wp-block-paragraph\">\u0622\u0645\u0644 \u0623\u0646 \u0623\u0643\u0648\u0646 \u0642\u062f \u0646\u062c\u062d\u062a \ud83d\ude01. \u0625\u0630\u0627 \u0641\u0639\u0644\u062a \u0630\u0644\u0643\u060c \u0641\u0633\u062a\u062a\u0628\u0639 \u0628\u0642\u064a\u0629 \u0627\u0644\u0645\u0642\u0627\u0644\u0629 \u0647\u0630\u0647 \u0627\u0644\u062e\u0637\u0648\u0627\u062a:<\/p>\n<ol class=\"wp-block-list\">\n<li class=\"wp-block-list-item\">\u0633\u0648\u0641 \u0646\u0646\u0627\u0642\u0634 <strong>\u0646\u0645\u0648\u0630\u062c Black-Scholes<\/strong>\u060c \u0648\u0627\u0641\u062a\u0631\u0627\u0636\u0627\u062a\u0647\u060c \u0648\u0645\u0639\u0627\u062f\u0644\u062a\u0647 \u0627\u0644\u062a\u0641\u0627\u0636\u0644\u064a\u0629<\/li>\n<li class=\"wp-block-list-item\">\u0633\u0648\u0641 \u0646\u062a\u062d\u062f\u062b \u0639\u0646 <strong>\u0627\u0644\u0634\u0628\u0643\u0627\u062a \u0627\u0644\u0639\u0635\u0628\u064a\u0629 \u0627\u0644\u0645\u0633\u062a\u0646\u062f\u0629 \u0625\u0644\u0649 \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621 (PINNs)<\/strong>\u060c \u0648\u0645\u0646 \u0623\u064a\u0646 \u0623\u062a\u062a\u060c \u0648\u0644\u0645\u0627\u0630\u0627 \u0647\u064a \u0645\u0641\u064a\u062f\u0629<\/li>\n<li class=\"wp-block-list-item\">\u0633\u0646\u0642\u0648\u0645 \u0628\u062a\u0637\u0648\u064a\u0631 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0627\u0644\u062e\u0627\u0635\u0629 \u0628\u0646\u0627 \u0627\u0644\u062a\u064a \u062a\u062f\u0631\u0628 PINN \u0639\u0644\u0649 Black-Scholes \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 <strong>Python<\/strong> \u0648 <strong>Torch<\/strong> \u0648 <strong>OOP<\/strong>.<\/li>\n<li class=\"wp-block-list-item\">\u0633\u0646\u0639\u0631\u0636 \u0646\u062a\u0627\u0626\u062c \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0627\u0644\u062e\u0627\u0635\u0629 \u0628\u0646\u0627.<\/li>\n<\/ol>\n<p class=\"wp-block-paragraph\">\u0623\u0646\u0627 \u0645\u062a\u062d\u0645\u0633! \u0625\u0644\u0649 \u0627\u0644\u0645\u062e\u062a\u0628\u0631! \ud83e\uddea<\/p>\n<h2 class=\"wp-block-heading\">1. \u0646\u0645\u0648\u0630\u062c \u0628\u0644\u0627\u0643 \u0633\u0643\u0648\u0644\u0632: \u0646\u0638\u0631\u0629 \u0645\u062a\u0639\u0645\u0642\u0629<\/h2>\n<p>&nbsp;<\/p>\n<blockquote><p>\u0625\u0630\u0627 \u0643\u0646\u062a \u0645\u0647\u062a\u0645\u064b\u0627 \u0628\u0627\u0644\u0627\u0637\u0644\u0627\u0639 \u0639\u0644\u0649 \u0627\u0644\u0648\u0631\u0642\u0629 \u0627\u0644\u0628\u062d\u062b\u064a\u0629 \u0627\u0644\u0623\u0635\u0644\u064a\u0629 \u0644\u0646\u0645\u0648\u0630\u062c \u0628\u0644\u0627\u0643-\u0634\u0648\u0644\u0632\u060c \u064a\u0645\u0643\u0646\u0643 \u0627\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u064a\u0647\u0627 <a target=\"_blank\" rel=\"noopener noreferrer\" href=\"https:\/\/www.cs.princeton.edu\/courses\/archive\/fall09\/cos323\/papers\/black_scholes73.pdf\">\u0647\u0646\u0627<\/a>. \u0628\u0627\u0644\u062a\u0623\u0643\u064a\u062f \u062a\u0633\u062a\u062d\u0642 \u0627\u0644\u0642\u0631\u0627\u0621\u0629 \ud83d\ude42<\/p><\/blockquote>\n<p class=\"wp-block-paragraph\">\u062d\u0633\u0646\u064b\u0627\u060c \u0627\u0644\u0622\u0646 \u064a\u062c\u0628 \u0623\u0646 \u0646\u0641\u0647\u0645 \u0639\u0627\u0644\u0645 <a target=\"_blank\" rel=\"noopener noreferrer\" title=\"Finance\" href=\"https:\/\/www.dztecs.com\/ai\/how-ai-is-redefining-education-the-future-of-work-and-funding-cuts\/\">\u0627\u0644\u062a\u0645\u0648\u064a\u0644<\/a> \u0627\u0644\u0630\u064a \u0646\u062d\u0646 \u0641\u064a\u0647\u060c \u0648\u0645\u0627 \u0647\u064a \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a\u060c \u0648\u0645\u0627 \u0647\u064a \u0627\u0644\u0642\u0648\u0627\u0646\u064a\u0646 \u0627\u0644\u062a\u064a \u062a\u062d\u0643\u0645\u0647. \u0641\u0647\u0645 \u0623\u0633\u0627\u0633\u064a\u0627\u062a \u0627\u0644\u062a\u0645\u0648\u064a\u0644 \u0648\u0639\u0644\u0627\u0642\u062a\u0647\u0627 \u0628\u0640 Black-Scholes \u0623\u0645\u0631 \u0628\u0627\u0644\u063a \u0627\u0644\u0623\u0647\u0645\u064a\u0629.<\/p>\n<p class=\"wp-block-paragraph\">\u0623\u0648\u0644\u0627\u064b\u060c \u0641\u064a \u0645\u062c\u0627\u0644 \u0627\u0644\u062a\u0645\u0648\u064a\u0644\u060c \u062a\u0648\u062c\u062f \u0623\u062f\u0627\u0629 \u0642\u0648\u064a\u0629 \u062a\u0633\u0645\u0649 <strong>\u062e\u064a\u0627\u0631<\/strong> \u0627\u0644\u0634\u0631\u0627\u0621 (call option). \u064a\u0645\u0646\u062d\u0643 \u062e\u064a\u0627\u0631 \u0627\u0644\u0634\u0631\u0627\u0621 \u0627\u0644\u062d\u0642 (\u0648\u0644\u064a\u0633 \u0627\u0644\u0627\u0644\u062a\u0632\u0627\u0645) \u0641\u064a \u0634\u0631\u0627\u0621 \u0633\u0647\u0645 \u0628\u0633\u0639\u0631 \u0645\u0639\u064a\u0646 \u0641\u064a \u0627\u0644\u0645\u0633\u062a\u0642\u0628\u0644 \u0627\u0644\u0645\u062d\u062f\u062f (\u0644\u0646\u0641\u062a\u0631\u0636 \u0628\u0639\u062f \u0639\u0627\u0645 \u0645\u0646 \u0627\u0644\u0622\u0646)\u060c \u0648\u0647\u0648 \u0645\u0627 \u064a\u0633\u0645\u0649 \u0628\u0633\u0639\u0631 \u0627\u0644\u062a\u0646\u0641\u064a\u0630 (strike <strong>price<\/strong>).<\/p>\n<p class=\"wp-block-paragraph\">\u0627\u0644\u0622\u0646\u060c \u062f\u0639\u0648\u0646\u0627 \u0646\u0641\u0643\u0631 \u0641\u064a \u0627\u0644\u0623\u0645\u0631 \u0644\u0644\u062d\u0638\u0629\u060c \u0623\u0644\u064a\u0633 \u0643\u0630\u0644\u0643\u061f \u0644\u0646\u0641\u062a\u0631\u0636 \u0623\u0646 \u0633\u0639\u0631 \u0627\u0644\u0633\u0647\u0645 \u0627\u0644\u064a\u0648\u0645 \u0647\u0648 100 \u062f\u0648\u0644\u0627\u0631. \u0644\u0646\u0641\u062a\u0631\u0636 \u0623\u064a\u0636\u064b\u0627 \u0623\u0646\u0646\u0627 \u0646\u0645\u062a\u0644\u0643 \u062e\u064a\u0627\u0631 \u0634\u0631\u0627\u0621 \u0628\u0633\u0639\u0631 \u062a\u0646\u0641\u064a\u0630 100 \u062f\u0648\u0644\u0627\u0631. \u0627\u0644\u0622\u0646\u060c \u0644\u0646\u0641\u062a\u0631\u0636 \u0623\u0646\u0647 \u0641\u064a \u063a\u0636\u0648\u0646 \u0639\u0627\u0645 \u0648\u0627\u062d\u062f\u060c \u0627\u0631\u062a\u0641\u0639 \u0633\u0639\u0631 \u0627\u0644\u0633\u0647\u0645 \u0625\u0644\u0649 150 \u062f\u0648\u0644\u0627\u0631\u064b\u0627. \u0647\u0630\u0627 \u0631\u0627\u0626\u0639! \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062e\u064a\u0627\u0631 \u0627\u0644\u0634\u0631\u0627\u0621 \u0647\u0630\u0627 \u0644\u0634\u0631\u0627\u0621 \u0627\u0644\u0633\u0647\u0645 \u062b\u0645 \u0625\u0639\u0627\u062f\u0629 \u0628\u064a\u0639\u0647 \u0639\u0644\u0649 \u0627\u0644\u0641\u0648\u0631! \u0644\u0642\u062f \u062d\u0642\u0642\u0646\u0627 \u0644\u0644\u062a\u0648 \u0631\u0628\u062d\u064b\u0627 \u0642\u062f\u0631\u0647 150 \u062f\u0648\u0644\u0627\u0631\u064b\u0627 &#8211; 100 \u062f\u0648\u0644\u0627\u0631 = 50 \u062f\u0648\u0644\u0627\u0631\u064b\u0627. \u0645\u0646 \u0646\u0627\u062d\u064a\u0629 \u0623\u062e\u0631\u0649\u060c \u0625\u0630\u0627 \u0627\u0646\u062e\u0641\u0636 \u0633\u0639\u0631 \u0627\u0644\u0633\u0647\u0645 \u0641\u064a \u063a\u0636\u0648\u0646 \u0639\u0627\u0645 \u0648\u0627\u062d\u062f \u0625\u0644\u0649 80 \u062f\u0648\u0644\u0627\u0631\u064b\u0627\u060c \u0641\u0644\u0627 \u064a\u0645\u0643\u0646\u0646\u0627 \u0641\u0639\u0644 \u0630\u0644\u0643. \u0641\u064a \u0627\u0644\u0648\u0627\u0642\u0639\u060c \u0645\u0646 \u0627\u0644\u0623\u0641\u0636\u0644 \u0644\u0646\u0627 \u0639\u062f\u0645 \u0645\u0645\u0627\u0631\u0633\u0629 \u062d\u0642\u0646\u0627 \u0641\u064a \u0627\u0644\u0634\u0631\u0627\u0621 \u0639\u0644\u0649 \u0627\u0644\u0625\u0637\u0644\u0627\u0642\u060c \u062d\u062a\u0649 \u0644\u0627 \u0646\u062e\u0633\u0631 \u0627\u0644\u0645\u0627\u0644.<\/p>\n<p class=\"wp-block-paragraph\">\u0625\u0630\u064b\u0627\u060c \u0628\u0639\u062f \u0623\u0646 \u0641\u0643\u0631\u0646\u0627 \u0641\u064a \u0627\u0644\u0623\u0645\u0631\u060c \u0641\u0625\u0646 \u0641\u0643\u0631\u0629 <strong>\u0634\u0631\u0627\u0621 \u0633\u0647\u0645<\/strong> \u0648 <strong>\u0628\u064a\u0639 \u062e\u064a\u0627\u0631<\/strong> \u062a\u0628\u062f\u0648 <strong>\u0645\u062a\u0643\u0627\u0645\u0644\u0629 \u062a\u0645\u0627\u0645\u064b\u0627<\/strong>. \u0645\u0627 \u0623\u0639\u0646\u064a\u0647 \u0647\u0648 \u0623\u0646 \u0639\u0634\u0648\u0627\u0626\u064a\u0629 \u0633\u0639\u0631 \u0627\u0644\u0633\u0647\u0645 (\u062d\u0642\u064a\u0642\u0629 \u0623\u0646\u0647 \u064a\u0631\u062a\u0641\u0639 \u0648\u064a\u0646\u062e\u0641\u0636) \u064a\u0645\u0643\u0646 \u0641\u064a \u0627\u0644\u0648\u0627\u0642\u0639 <strong>\u062a\u062e\u0641\u064a\u0641\u0647\u0627<\/strong> \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u0627\u062d\u062a\u0641\u0627\u0638 \u0628\u0627\u0644\u0639\u062f\u062f \u0627\u0644\u0635\u062d\u064a\u062d \u0645\u0646 \u0627\u0644\u062e\u064a\u0627\u0631\u0627\u062a. \u0648\u0647\u0630\u0627 \u0645\u0627 \u064a\u0633\u0645\u0649 <strong>\u0628\u0627\u0644\u062a\u062d\u0648\u0637 \u0627\u0644\u062f\u0644\u062a\u0627 (delta hedging).<\/strong> \u0648\u0647\u0648 \u0627\u0633\u062a\u0631\u0627\u062a\u064a\u062c\u064a\u0629 \u0623\u0633\u0627\u0633\u064a\u0629 \u0641\u064a \u0625\u062f\u0627\u0631\u0629 \u0627\u0644\u0645\u062e\u0627\u0637\u0631.<\/p>\n<p class=\"wp-block-paragraph\">\u0628\u0646\u0627\u0621\u064b \u0639\u0644\u0649 \u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u0646 \u0627\u0644\u0627\u0641\u062a\u0631\u0627\u0636\u0627\u062a\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0634\u062a\u0642\u0627\u0642 <strong>\u0633\u0639\u0631 \u0627\u0644\u062e\u064a\u0627\u0631 \u0627\u0644\u0639\u0627\u062f\u0644<\/strong> \u0645\u0646 \u0623\u062c\u0644 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0645\u062d\u0641\u0638\u0629 <strong>\u062e\u0627\u0644\u064a\u0629 \u0645\u0646 \u0627\u0644\u0645\u062e\u0627\u0637\u0631<\/strong>. \u0647\u0630\u0627 \u0627\u0644\u0645\u0641\u0647\u0648\u0645 \u062c\u0648\u0647\u0631\u064a \u0644\u0646\u0645\u0648\u0630\u062c Black-Scholes.<\/p>\n<p class=\"wp-block-paragraph\">\u0644\u0627 \u0623\u0631\u064a\u062f \u0623\u0646 \u0623\u0645\u0644\u0651\u0643 \u0628\u0643\u0644 \u062a\u0641\u0627\u0635\u064a\u0644 \u0627\u0644\u0627\u0634\u062a\u0642\u0627\u0642 (\u0628\u0635\u0631\u0627\u062d\u0629\u060c \u0644\u064a\u0633 \u0645\u0646 \u0627\u0644\u0635\u0639\u0628 \u0645\u062a\u0627\u0628\u0639\u062a\u0647\u0627 \u0641\u064a \u0627\u0644\u0648\u0631\u0642\u0629 \u0627\u0644\u0623\u0635\u0644\u064a\u0629)\u060c \u0648\u0644\u0643\u0646 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u062a\u0641\u0627\u0636\u0644\u064a\u0629 \u0644\u0644\u0645\u062d\u0641\u0638\u0629 \u0627\u0644\u062e\u0627\u0644\u064a\u0629 \u0645\u0646 \u0627\u0644\u0645\u062e\u0627\u0637\u0631 \u0647\u064a \u0647\u0630\u0647:<\/p>\n<p><img decoding=\"async\" class=\"wp-image-601650 aligncenter\" src=\"https:\/\/www.dztecs.com\/ai\/wp-content\/uploads\/sites\/2\/2025\/05\/Differential_Equation_BS-1024x129-1.png\" alt=\"\" \/ width=\"1024\" height=\"129\"><\/p>\n<p class=\"wp-block-paragraph\">\u062d\u064a\u062b:<\/p>\n<ul class=\"wp-block-list\">\n<li class=\"wp-block-list-item\"><code>C<\/code> \u0647\u0648 \u0633\u0639\u0631 \u0627\u0644\u062e\u064a\u0627\u0631 \u0641\u064a \u0627\u0644\u0648\u0642\u062a t<\/li>\n<li class=\"wp-block-list-item\"><code>sigma<\/code> \u0647\u0648 \u062a\u0642\u0644\u0628 \u0627\u0644\u0633\u0647\u0645<\/li>\n<li class=\"wp-block-list-item\"><code>r<\/code> \u0647\u0648 \u0627\u0644\u0645\u0639\u062f\u0644 \u0627\u0644\u062e\u0627\u0644\u064a \u0645\u0646 \u0627\u0644\u0645\u062e\u0627\u0637\u0631<\/li>\n<li class=\"wp-block-list-item\"><code>t<\/code> \u0647\u0648 \u0627\u0644\u0648\u0642\u062a (\u0645\u0639 t=0 \u0627\u0644\u0622\u0646 \u0648 T \u0639\u0646\u062f \u062a\u0627\u0631\u064a\u062e \u0627\u0644\u0627\u0646\u062a\u0647\u0627\u0621)<\/li>\n<li class=\"wp-block-list-item\"><code>S<\/code> \u0647\u0648 \u0633\u0639\u0631 \u0627\u0644\u0633\u0647\u0645 \u0627\u0644\u062d\u0627\u0644\u064a<\/li>\n<\/ul>\n<p class=\"wp-block-paragraph\">\u0645\u0646 \u0647\u0630\u0647 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0634\u062a\u0642\u0627\u0642 \u0627\u0644\u0633\u0639\u0631 \u0627\u0644\u0639\u0627\u062f\u0644 \u0644\u062e\u064a\u0627\u0631 \u0627\u0644\u0634\u0631\u0627\u0621 \u0644\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0645\u062d\u0641\u0638\u0629 \u062e\u0627\u0644\u064a\u0629 \u0645\u0646 \u0627\u0644\u0645\u062e\u0627\u0637\u0631. \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0645\u063a\u0644\u0642\u0629 \u0648\u062a\u062d\u0644\u064a\u0644\u064a\u0629\u060c \u0648\u062a\u0628\u062f\u0648 \u0647\u0643\u0630\u0627:<\/p>\n<p><img decoding=\"async\" class=\"wp-image-601654 aligncenter\" style=\"width: 486px; height: auto;\" src=\"https:\/\/www.dztecs.com\/ai\/wp-content\/uploads\/sites\/2\/2025\/05\/Black_Scholes_Solution-1024x100-1.png\" alt=\"\" \/ width=\"1024\" height=\"100\"><\/p>\n<p class=\"wp-block-paragraph\">\u0645\u0639:<\/p>\n<p><img decoding=\"async\" class=\"wp-image-601655 aligncenter\" style=\"width: 377px; height: auto;\" src=\"https:\/\/www.dztecs.com\/ai\/wp-content\/uploads\/sites\/2\/2025\/05\/d1_and_d2-1024x378-1.png\" alt=\"\" \/ width=\"1024\" height=\"378\"><\/p>\n<p class=\"wp-block-paragraph\">\u062d\u064a\u062b N(x) \u0647\u064a \u062f\u0627\u0644\u0629 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u062a\u0631\u0627\u0643\u0645\u064a (CDF) \u0644\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0637\u0628\u064a\u0639\u064a \u0627\u0644\u0642\u064a\u0627\u0633\u064a\u060c K \u0647\u0648 \u0633\u0639\u0631 \u0627\u0644\u062a\u0646\u0641\u064a\u0630\u060c \u0648 T \u0647\u0648 \u062a\u0627\u0631\u064a\u062e \u0627\u0644\u0627\u0646\u062a\u0647\u0627\u0621.<\/p>\n<p class=\"wp-block-paragraph\">\u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0647\u0630\u0627 \u0647\u0648 \u0645\u062e\u0637\u0637 <strong>\u0633\u0639\u0631 \u0627\u0644\u0633\u0647\u0645 (x)<\/strong> \u0645\u0642\u0627\u0628\u0644 <strong><strong>\u062e\u064a\u0627\u0631 \u0627\u0644\u0634\u0631\u0627\u0621 (y)<\/strong><\/strong>\u060c \u0648\u0641\u0642\u064b\u0627 \u0644\u0646\u0645\u0648\u0630\u062c \u0628\u0644\u0627\u0643-\u0634\u0648\u0644\u0632.<\/p>\n<p><img decoding=\"async\" class=\"wp-image-601656 aligncenter\" src=\"https:\/\/www.dztecs.com\/ai\/wp-content\/uploads\/sites\/2\/2025\/05\/image-49.png\" alt=\"\" \/ width=\"989\" height=\"590\"><\/p>\n<p class=\"wp-block-paragraph\">\u0627\u0644\u0622\u0646 \u0647\u0630\u0627 \u064a\u0628\u062f\u0648 \u0631\u0627\u0626\u0639\u064b\u0627 \u0648\u0643\u0644 \u0634\u064a\u0621\u060c \u0648\u0644\u0643\u0646 \u0645\u0627 \u0639\u0644\u0627\u0642\u0629 \u0647\u0630\u0627 \u0628\u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621 \u0648 PINN\u061f \u064a\u0628\u062f\u0648 \u0623\u0646 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u062a\u062d\u0644\u064a\u0644\u064a\u0629\u060c \u0641\u0644\u0645\u0627\u0630\u0627 PINN\u061f \u0644\u0645\u0627\u0630\u0627 \u0627\u0644\u0630\u0643\u0627\u0621 \u0627\u0644\u0627\u0635\u0637\u0646\u0627\u0639\u064a\u061f \u0644\u0645\u0627\u0630\u0627 \u0623\u0642\u0631\u0623 \u0647\u0630\u0627 \u0639\u0644\u0649 \u0627\u0644\u0625\u0637\u0644\u0627\u0642\u061f \u0627\u0644\u062c\u0648\u0627\u0628 \u0623\u062f\u0646\u0627\u0647 \ud83d\udc47:<\/p>\n<p>&nbsp;<\/p>\n<h2 class=\"wp-block-heading\">2. \u0627\u0644\u0634\u0628\u0643\u0627\u062a \u0627\u0644\u0639\u0635\u0628\u064a\u0629 \u0627\u0644\u0645\u064f\u0633\u062a\u0646\u064a\u0631\u0629 \u0628\u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621 (Physics Informed Neural Networks)<\/h2>\n<p>&nbsp;<\/p>\n<blockquote><p>\u0625\u0630\u0627 \u0643\u0646\u062a \u0645\u0647\u062a\u0645\u064b\u0627 \u0628\u0627\u0644\u0634\u0628\u0643\u0627\u062a \u0627\u0644\u0639\u0635\u0628\u064a\u0629 \u0627\u0644\u0645\u0633\u062a\u0646\u064a\u0631\u0629 \u0628\u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621 (Physics Informed Neural Networks &#8211; PINNs)\u060c \u064a\u0645\u0643\u0646\u0643 \u0627\u0644\u0627\u0637\u0644\u0627\u0639 \u0639\u0644\u0649 \u0627\u0644\u0648\u0631\u0642\u0629 \u0627\u0644\u0623\u0635\u0644\u064a\u0629 <a target=\"_blank\" rel=\"noopener noreferrer\" href=\"http:\/\/Physics%20Informed%20Neural%20Networks\">\u0647\u0646\u0627<\/a>. \u0645\u0631\u0629 \u0623\u062e\u0631\u0649\u060c \u062a\u0633\u062a\u062d\u0642 \u0627\u0644\u0642\u0631\u0627\u0621\u0629. \ud83d\ude42<\/p><\/blockquote>\n<p class=\"wp-block-paragraph\">\u0627\u0644\u0622\u0646\u060c \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0623\u0639\u0644\u0627\u0647 <strong>\u062a\u062d\u0644\u064a\u0644\u064a\u0629<\/strong>\u060c \u0648\u0644\u0643\u0646 \u0645\u0631\u0629 \u0623\u062e\u0631\u0649\u060c \u0647\u0630\u0647 \u0645\u0639\u0627\u062f\u0644\u0629 \u0644\u0633\u0639\u0631 \u0639\u0627\u062f\u0644 \u0641\u064a \u0633\u064a\u0646\u0627\u0631\u064a\u0648 \u0645\u062b\u0627\u0644\u064a. \u0645\u0627\u0630\u0627 \u064a\u062d\u062f\u062b \u0625\u0630\u0627 \u062a\u062c\u0627\u0647\u0644\u0646\u0627 \u0647\u0630\u0627 \u0644\u0644\u062d\u0638\u0629 \u0648\u062d\u0627\u0648\u0644\u0646\u0627 \u062a\u062e\u0645\u064a\u0646 \u0633\u0639\u0631 \u0627\u0644\u062e\u064a\u0627\u0631 \u0628\u0646\u0627\u0621\u064b \u0639\u0644\u0649 \u0633\u0639\u0631 \u0627\u0644\u0633\u0647\u0645 \u0648\u0627\u0644\u0648\u0642\u062a\u061f \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0634\u0628\u0643\u0629 \u0639\u0635\u0628\u064a\u0629 \u062a\u063a\u0630\u064a\u0629 \u0623\u0645\u0627\u0645\u064a\u0629 (Feed Forward Neural Network) \u0648\u062a\u062f\u0631\u064a\u0628\u0647\u0627 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u0627\u0646\u062a\u0634\u0627\u0631 \u0627\u0644\u062e\u0644\u0641\u064a (backpropagation). \u0647\u0630\u0627 \u0627\u0644\u0646\u0647\u062c \u064a\u0645\u062b\u0644 \u0623\u0633\u0627\u0633 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0634\u0628\u0643\u0627\u062a \u0627\u0644\u0639\u0635\u0628\u064a\u0629 \u0641\u064a \u062a\u0633\u0639\u064a\u0631 \u0627\u0644\u062e\u064a\u0627\u0631\u0627\u062a.<\/p>\n<p class=\"wp-block-paragraph\">\u0641\u064a \u0622\u0644\u064a\u0629 \u0627\u0644\u062a\u062f\u0631\u064a\u0628 \u0647\u0630\u0647\u060c \u0646\u0642\u0648\u0645 \u0628\u062a\u0642\u0644\u064a\u0644 \u0627\u0644\u062e\u0637\u0623:<\/p>\n<p class=\"wp-block-paragraph\"><code>L = |Estimated C - Real C|<\/code>:<\/p>\n<p><img decoding=\"async\" class=\"wp-image-601671 aligncenter\" src=\"https:\/\/www.dztecs.com\/ai\/wp-content\/uploads\/sites\/2\/2025\/05\/image-50-1024x645-1.png\" alt=\"\" \/ width=\"1024\" height=\"645\"><\/p>\n<p class=\"wp-block-paragraph\">\u0647\u0630\u0627 \u062c\u064a\u062f\u060c \u0648\u0647\u0648 \u0623\u0628\u0633\u0637 \u0646\u0647\u062c \u0644\u0644\u0634\u0628\u0643\u0627\u062a \u0627\u0644\u0639\u0635\u0628\u064a\u0629 \u064a\u0645\u0643\u0646\u0643 \u0627\u0644\u0642\u064a\u0627\u0645 \u0628\u0647. \u0627\u0644\u0645\u0634\u0643\u0644\u0629 \u0647\u0646\u0627 \u0647\u064a \u0623\u0646\u0646\u0627 \u0646\u062a\u062c\u0627\u0647\u0644 \u062a\u0645\u0627\u0645\u064b\u0627 \u0645\u0639\u0627\u062f\u0644\u0629 \u0628\u0644\u0627\u0643-\u0634\u0648\u0644\u0632 (Black-Scholes equation). \u0625\u0630\u0646\u060c \u0647\u0644 \u0647\u0646\u0627\u0643 \u0637\u0631\u064a\u0642\u0629 \u0623\u062e\u0631\u0649\u061f \u0647\u0644 \u064a\u0645\u0643\u0646\u0646\u0627 \u062f\u0645\u062c\u0647\u0627\u061f<\/p>\n<p class=\"wp-block-paragraph\">\u0628\u0627\u0644\u0637\u0628\u0639\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0630\u0644\u0643\u060c \u0625\u0630\u0627 \u0642\u0645\u0646\u0627 \u0628\u062a\u0639\u064a\u064a\u0646 \u0627\u0644\u062e\u0637\u0623 \u0644\u064a\u0643\u0648\u0646:<\/p>\n<p class=\"wp-block-paragraph\"><code>L = |Estimated C - Real C|+ PDE(C,S,t)<\/code><\/p>\n<p class=\"wp-block-paragraph\">\u062d\u064a\u062b PDE(C,S,t) \u0647\u064a:<\/p>\n<p><img decoding=\"async\" class=\"wp-image-601650 aligncenter\" src=\"https:\/\/www.dztecs.com\/ai\/wp-content\/uploads\/sites\/2\/2025\/05\/Differential_Equation_BS-1024x129-1.png\" alt=\"\" \/ width=\"1024\" height=\"129\"><\/p>\n<p class=\"wp-block-paragraph\">\u0648\u064a\u062c\u0628 \u0623\u0646 \u062a\u0643\u0648\u0646 \u0642\u0631\u064a\u0628\u0629 \u0645\u0646 0 \u0642\u062f\u0631 \u0627\u0644\u0625\u0645\u0643\u0627\u0646:<\/p>\n<p><img decoding=\"async\" class=\"wp-image-601673 aligncenter\" src=\"https:\/\/www.dztecs.com\/ai\/wp-content\/uploads\/sites\/2\/2025\/05\/image-52-1024x638-1.png\" alt=\"\" \/ width=\"1024\" height=\"638\"><\/p>\n<p class=\"wp-block-paragraph\">\u0648\u0644\u0643\u0646 \u0627\u0644\u0633\u0624\u0627\u0644 \u0644\u0627 \u064a\u0632\u0627\u0644 \u0642\u0627\u0626\u0645\u0627. \u0644\u0645\u0627\u0630\u0627 \u0647\u0630\u0627 &#8220;\u0623\u0641\u0636\u0644&#8221; \u0645\u0646 \u0645\u0639\u0627\u062f\u0644\u0629 \u0628\u0644\u0627\u0643-\u0634\u0648\u0644\u0632 \u0627\u0644\u0628\u0633\u064a\u0637\u0629\u061f \u0644\u0645\u0627\u0630\u0627 \u0644\u0627 \u0646\u0633\u062a\u062e\u062f\u0645 \u0641\u0642\u0637 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u062a\u0641\u0627\u0636\u0644\u064a\u0629\u061f \u062d\u0633\u0646\u064b\u0627\u060c \u0644\u0623\u0646\u0647 \u0641\u064a \u0628\u0639\u0636 \u0627\u0644\u0623\u062d\u064a\u0627\u0646\u060c \u0641\u064a \u0627\u0644\u062d\u064a\u0627\u0629\u060c \u0644\u0627 \u064a\u0636\u0645\u0646 \u0644\u0643 \u062d\u0644 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u062a\u0641\u0627\u0636\u0644\u064a\u0629 \u0627\u0644\u062d\u0644 &#8220;\u0627\u0644\u062d\u0642\u064a\u0642\u064a&#8221;. \u0639\u0627\u062f\u0629\u064b \u0645\u0627 \u062a\u0642\u0648\u0645 \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621 \u0628\u062a\u0642\u0631\u064a\u0628 \u0627\u0644\u0623\u0634\u064a\u0627\u0621\u060c \u0648\u0647\u064a \u062a\u0641\u0639\u0644 \u0630\u0644\u0643 \u0628\u0637\u0631\u064a\u0642\u0629 \u064a\u0645\u0643\u0646 \u0623\u0646 \u062a\u062e\u0644\u0642 \u0641\u0631\u0642\u064b\u0627 \u0628\u064a\u0646 \u0645\u0627 \u0646\u062a\u0648\u0642\u0639\u0647 \u0648\u0645\u0627 \u0646\u0631\u0627\u0647. \u0644\u0647\u0630\u0627 \u0627\u0644\u0633\u0628\u0628 \u062a\u0639\u062a\u0628\u0631 \u0627\u0644\u0634\u0628\u0643\u0627\u062a \u0627\u0644\u0639\u0635\u0628\u064a\u0629 \u0627\u0644\u0645\u0633\u062a\u0646\u064a\u0631\u0629 \u0628\u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621 (PINN) \u0623\u062f\u0627\u0629 \u0645\u062f\u0647\u0634\u0629 \u0648\u0631\u0627\u0626\u0639\u0629: \u0641\u0623\u0646\u062a \u062a\u062d\u0627\u0648\u0644 \u0645\u0637\u0627\u0628\u0642\u0629 \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621\u060c \u0644\u0643\u0646\u0643 \u0635\u0627\u0631\u0645 \u0641\u064a \u062d\u0642\u064a\u0642\u0629 \u0623\u0646 \u0627\u0644\u0646\u062a\u0627\u0626\u062c \u064a\u062c\u0628 \u0623\u0646 \u062a\u062a\u0637\u0627\u0628\u0642 \u0645\u0639 \u0645\u0627 &#8220;\u062a\u0631\u0627\u0647&#8221; \u0645\u0646 \u0645\u062c\u0645\u0648\u0639\u0629 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u062e\u0627\u0635\u0629 \u0628\u0643. \u0647\u0630\u0627 \u0627\u0644\u062a\u0643\u0627\u0645\u0644 \u0628\u064a\u0646 \u0627\u0644\u0646\u0645\u0648\u0630\u062c \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0626\u064a \u0648\u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u062a\u062c\u0631\u064a\u0628\u064a\u0629 \u0647\u0648 \u0645\u0627 \u064a\u0645\u064a\u0632 \u0647\u0630\u0627 \u0627\u0644\u0646\u0647\u062c.<\/p>\n<p class=\"wp-block-paragraph\">\u0641\u064a \u062d\u0627\u0644\u062a\u0646\u0627\u060c \u0642\u062f \u064a\u0643\u0648\u0646 \u0627\u0644\u0623\u0645\u0631 \u0623\u0646\u0647 \u0645\u0646 \u0623\u062c\u0644 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0645\u062d\u0641\u0638\u0629 \u062e\u0627\u0644\u064a\u0629 \u0645\u0646 \u0627\u0644\u0645\u062e\u0627\u0637\u0631\u060c \u0646\u062c\u062f \u0623\u0646 \u0646\u0645\u0648\u0630\u062c \u0628\u0644\u0627\u0643-\u0634\u0648\u0644\u0632 \u0627\u0644\u0646\u0638\u0631\u064a \u0644\u0627 \u064a\u062a\u0637\u0627\u0628\u0642 \u062a\u0645\u0627\u0645\u064b\u0627 \u0645\u0639 \u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0633\u0648\u0642 \u0627\u0644\u0635\u0627\u062e\u0628\u0629 \u0623\u0648 \u0627\u0644\u0645\u062a\u062d\u064a\u0632\u0629 \u0623\u0648 \u063a\u064a\u0631 \u0627\u0644\u0643\u0627\u0645\u0644\u0629 \u0627\u0644\u062a\u064a \u0646\u0631\u0627\u0642\u0628\u0647\u0627. \u0631\u0628\u0645\u0627 \u0627\u0644\u062a\u0642\u0644\u0628 \u0644\u064a\u0633 \u062b\u0627\u0628\u062a\u064b\u0627. \u0631\u0628\u0645\u0627 \u0627\u0644\u0633\u0648\u0642 \u0644\u064a\u0633 \u0641\u0639\u0627\u0644\u0627\u064b. \u0631\u0628\u0645\u0627 \u0627\u0644\u0627\u0641\u062a\u0631\u0627\u0636\u0627\u062a \u0627\u0644\u0643\u0627\u0645\u0646\u0629 \u0648\u0631\u0627\u0621 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0644\u0627 \u062a\u0635\u0645\u062f. \u0647\u0630\u0627 \u0647\u0648 \u0627\u0644\u0645\u0643\u0627\u0646 \u0627\u0644\u0630\u064a \u064a\u0645\u0643\u0646 \u0623\u0646 \u064a\u0643\u0648\u0646 \u0641\u064a\u0647 \u0646\u0647\u062c \u0645\u062b\u0644 PINN \u0645\u0641\u064a\u062f\u064b\u0627. \u0646\u062d\u0646 \u0644\u0627 \u0646\u062c\u062f \u062d\u0644\u0627\u064b \u064a\u0641\u064a \u0628\u0645\u0639\u0627\u062f\u0644\u0629 \u0628\u0644\u0627\u0643-\u0634\u0648\u0644\u0632 \u0641\u062d\u0633\u0628\u060c \u0628\u0644 &#8220;\u0646\u062b\u0642&#8221; \u0623\u064a\u0636\u064b\u0627 \u0628\u0645\u0627 \u0646\u0631\u0627\u0647 \u0645\u0646 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a. \u0647\u0630\u0627 \u064a\u0633\u0645\u062d \u0628\u0646\u0645\u0648\u0630\u062c \u0623\u0643\u062b\u0631 \u0645\u0631\u0648\u0646\u0629 \u0648\u0642\u0627\u0628\u0644\u064a\u0629 \u0644\u0644\u062a\u0643\u064a\u0641 \u0645\u0639 \u0638\u0631\u0648\u0641 \u0627\u0644\u0633\u0648\u0642 \u0627\u0644\u062d\u0642\u064a\u0642\u064a\u0629.<\/p>\n<p class=\"wp-block-paragraph\">\u062d\u0633\u0646\u064b\u0627\u060c \u064a\u0643\u0641\u064a \u0645\u0646 \u0627\u0644\u0646\u0638\u0631\u064a\u0629. \u0647\u064a\u0627 \u0646\u0628\u0631\u0645\u062c. \ud83d\udc68\u200d\ud83d\udcbb<\/p>\n<p>&nbsp;<\/p>\n<h2 class=\"wp-block-heading\">3. \u062a\u0637\u0628\u064a\u0642 \u0639\u0645\u0644\u064a \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 Python<\/h2>\n<blockquote><p>\u064a\u0645\u0643\u0646\u0643 \u0627\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 \u0627\u0644\u0643\u0648\u062f \u0627\u0644\u0643\u0627\u0645\u0644\u060c \u0645\u0639 \u0645\u0644\u0641 README.md \u0631\u0627\u0626\u0639\u060c \u0648\u062f\u0641\u062a\u0631 \u0645\u0644\u0627\u062d\u0638\u0627\u062a \u0645\u0645\u062a\u0627\u0632\u060c \u0648\u0643\u0648\u062f \u0645\u0639\u064a\u0627\u0631\u064a \u0641\u0627\u0626\u0642 \u0627\u0644\u0648\u0636\u0648\u062d <a target=\"_blank\" rel=\"noopener noreferrer\" href=\"https:\/\/github.com\/PieroPaialungaAI\/BlackScholesPINN\">\u0647\u0646\u0627<\/a>. \u0647\u0630\u0627 \u0627\u0644\u0643\u0648\u062f \u0645\u0635\u0645\u0645 \u062e\u0635\u064a\u0635\u064b\u0627 \u0644\u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0629 \u0628\u0644\u0627\u0643-\u0634\u0648\u0644\u0632 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0634\u0628\u0643\u0627\u062a PINN \u0627\u0644\u0639\u0635\u0628\u064a\u0629\u060c \u0648\u0647\u0648 \u0623\u0633\u0644\u0648\u0628 \u0645\u062a\u0642\u062f\u0645 \u0641\u064a \u0645\u062c\u0627\u0644 \u0627\u0644\u0646\u0645\u0630\u062c\u0629 \u0627\u0644\u0645\u0627\u0644\u064a\u0629.<\/p>\n<p>\u0645\u0644\u0627\u062d\u0638\u0629: \u0633\u064a\u0643\u0648\u0646 \u0647\u0630\u0627 \u0627\u0644\u062c\u0632\u0621 \u0645\u0643\u062b\u0641\u064b\u0627 \u0628\u0639\u0636 \u0627\u0644\u0634\u064a\u0621 (\u0627\u0644\u0643\u062b\u064a\u0631 \u0645\u0646 \u0627\u0644\u062a\u0639\u0644\u064a\u0645\u0627\u062a \u0627\u0644\u0628\u0631\u0645\u062c\u064a\u0629)\u060c \u0648\u0625\u0630\u0627 \u0644\u0645 \u062a\u0643\u0646 \u0645\u0647\u062a\u0645\u064b\u0627 \u0628\u0627\u0644\u0628\u0631\u0645\u062c\u064a\u0627\u062a\u060c \u0641\u0644\u0627 \u062a\u062a\u0631\u062f\u062f \u0641\u064a \u0627\u0644\u0627\u0646\u062a\u0642\u0627\u0644 \u0625\u0644\u0649 \u0627\u0644\u0641\u0635\u0644 \u0627\u0644\u062a\u0627\u0644\u064a. \u0633\u0623\u0639\u0631\u0636 \u0627\u0644\u0646\u062a\u0627\u0626\u062c \u0628\u0637\u0631\u064a\u0642\u0629 \u0623\u0643\u062b\u0631 \u0633\u0647\u0648\u0644\u0629 \ud83d\ude42<\/p><\/blockquote>\n<p class=\"wp-block-paragraph\">\u0634\u0643\u0631\u064b\u0627 \u062c\u0632\u064a\u0644\u0627\u064b \u0644\u0643 \u0639\u0644\u0649 \u0648\u0635\u0648\u0644\u0643 \u0625\u0644\u0649 \u0647\u0630\u0647 \u0627\u0644\u0645\u0631\u062d\u0644\u0629 \u2764\ufe0f<br \/>\n\u062f\u0639\u0646\u0627 \u0646\u0631\u0649 \u0643\u064a\u0641 \u064a\u0645\u0643\u0646\u0646\u0627 \u062a\u0646\u0641\u064a\u0630 \u0630\u0644\u0643. \u0644\u0646\u0633\u062a\u0639\u0631\u0636 \u0627\u0644\u0622\u0646 \u0643\u064a\u0641\u064a\u0629 \u062a\u0637\u0628\u064a\u0642 \u0647\u0630\u0647 \u0627\u0644\u062a\u0642\u0646\u064a\u0629 \u0641\u064a \u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0628\u0644\u0627\u0643-\u0634\u0648\u0644\u0632\u060c \u0645\u0639 \u0627\u0644\u062a\u0631\u0643\u064a\u0632 \u0639\u0644\u0649 \u0627\u0644\u062c\u0648\u0627\u0646\u0628 \u0627\u0644\u0639\u0645\u0644\u064a\u0629 \u0648\u0627\u0644\u062a\u0641\u0635\u064a\u0644\u064a\u0629.<\/p>\n<h3 class=\"wp-block-heading\">3.1 \u0645\u0644\u0641 Config.json<\/h3>\n<p class=\"wp-block-paragraph\">\u064a\u0645\u0643\u0646 \u062a\u0634\u063a\u064a\u0644 \u0627\u0644\u0643\u0648\u062f \u0628\u0627\u0644\u0643\u0627\u0645\u0644 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u0644\u0641 \u062a\u0647\u064a\u0626\u0629 \u0628\u0633\u064a\u0637 \u0644\u0644\u063a\u0627\u064a\u0629\u060c \u0623\u0637\u0644\u0642\u062a \u0639\u0644\u064a\u0647 \u0627\u0633\u0645 <strong>config.json<\/strong>.<\/p>\n<p class=\"wp-block-paragraph\">\u064a\u0645\u0643\u0646\u0643 \u0648\u0636\u0639\u0647 \u0641\u064a \u0623\u064a \u0645\u0643\u0627\u0646 \u062a\u0631\u064a\u062f\u0647\u060c \u0643\u0645\u0627 \u0633\u0646\u0631\u0649 \u0644\u0627\u062d\u0642\u064b\u0627.<\/p>\n<p class=\"wp-block-paragraph\">\u0647\u0630\u0627 \u0627\u0644\u0645\u0644\u0641 \u0636\u0631\u0648\u0631\u064a\u060c \u0644\u0623\u0646\u0647 \u064a\u062d\u062f\u062f \u062c\u0645\u064a\u0639 \u0627\u0644\u0645\u0639\u0644\u0645\u0627\u062a \u0627\u0644\u062a\u064a \u062a\u062d\u0643\u0645 \u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629 \u0627\u0644\u062e\u0627\u0635\u0629 \u0628\u0646\u0627\u060c \u0648\u062a\u0648\u0644\u064a\u062f \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a\u060c \u0648\u062a\u062f\u0631\u064a\u0628 \u0627\u0644\u0646\u0645\u0648\u0630\u062c. \u062f\u0639\u0646\u064a \u0623\u0634\u0631\u062d \u0644\u0643 \u0628\u0633\u0631\u0639\u0629 \u0645\u0627 \u062a\u0645\u062b\u0644\u0647 \u0643\u0644 \u0642\u064a\u0645\u0629:<\/p>\n<ul class=\"wp-block-list\">\n<li class=\"wp-block-list-item\"><code>K<\/code>: <strong>\u0633\u0639\u0631 \u0627\u0644\u062a\u0646\u0641\u064a\u0630<\/strong> \u2013 \u0648\u0647\u0648 \u0627\u0644\u0633\u0639\u0631 \u0627\u0644\u0630\u064a \u064a\u0645\u0646\u062d\u0643 \u0639\u0646\u062f\u0647 \u0627\u0644\u062e\u064a\u0627\u0631 \u0627\u0644\u062d\u0642 \u0641\u064a \u0634\u0631\u0627\u0621 \u0627\u0644\u0633\u0647\u0645 \u0641\u064a \u0627\u0644\u0645\u0633\u062a\u0642\u0628\u0644.<\/li>\n<li class=\"wp-block-list-item\"><code>T<\/code>: <strong>\u0627\u0644\u0648\u0642\u062a \u062d\u062a\u0649 \u062a\u0627\u0631\u064a\u062e \u0627\u0644\u0627\u0633\u062a\u062d\u0642\u0627\u0642<\/strong>\u060c \u0628\u0627\u0644\u0633\u0646\u0648\u0627\u062a. \u0625\u0630\u0646 <code>T = 1.0<\/code> \u064a\u0639\u0646\u064a \u0623\u0646 \u0635\u0644\u0627\u062d\u064a\u0629 \u0627\u0644\u062e\u064a\u0627\u0631 \u062a\u0646\u062a\u0647\u064a \u0628\u0639\u062f \u0648\u062d\u062f\u0629 \u0648\u0627\u062d\u062f\u0629 (\u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0633\u0646\u0629 \u0648\u0627\u062d\u062f\u0629) \u0645\u0646 \u0627\u0644\u0622\u0646.<\/li>\n<li class=\"wp-block-list-item\"><code>r<\/code>: <strong>\u0645\u0639\u062f\u0644 \u0627\u0644\u0641\u0627\u0626\u062f\u0629 \u0627\u0644\u062e\u0627\u0644\u064a \u0645\u0646 \u0627\u0644\u0645\u062e\u0627\u0637\u0631<\/strong> \u0627\u0644\u0645\u0633\u062a\u062e\u062f\u0645 \u0644\u062e\u0635\u0645 \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0645\u0633\u062a\u0642\u0628\u0644\u064a\u0629. \u0647\u0630\u0627 \u0647\u0648 \u0645\u0639\u062f\u0644 \u0627\u0644\u0641\u0627\u0626\u062f\u0629 \u0627\u0644\u0630\u064a \u0646\u062d\u062f\u062f\u0647 \u0641\u064a \u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629 \u0627\u0644\u062e\u0627\u0635\u0629 \u0628\u0646\u0627.<\/li>\n<li class=\"wp-block-list-item\"><code>sigma<\/code>: <strong>\u062a\u0642\u0644\u0628<\/strong> \u0627\u0644\u0633\u0647\u0645\u060c \u0648\u0627\u0644\u0630\u064a \u064a\u062d\u062f\u062f \u0645\u062f\u0649 \u0635\u0639\u0648\u0628\u0629 \u0627\u0644\u062a\u0646\u0628\u0624 \u0628\u0633\u0639\u0631 \u0627\u0644\u0633\u0647\u0645 \u0623\u0648 \u0645\u062f\u0649 &#8220;\u062e\u0637\u0648\u0631\u062a\u0647&#8221;. \u0645\u0631\u0629 \u0623\u062e\u0631\u0649\u060c \u0647\u0630\u0647 \u0645\u0639\u0644\u0645\u0629 \u0645\u062d\u0627\u0643\u0627\u0629.<\/li>\n<li class=\"wp-block-list-item\"><code>N_data<\/code>: \u0639\u062f\u062f <strong>\u0646\u0642\u0627\u0637 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0627\u0635\u0637\u0646\u0627\u0639\u064a\u0629<\/strong> \u0627\u0644\u062a\u064a \u0646\u0631\u064a\u062f \u0625\u0646\u0634\u0627\u0624\u0647\u0627 \u0644\u0644\u062a\u062f\u0631\u064a\u0628. \u0633\u064a\u062d\u062f\u062f \u0647\u0630\u0627 \u0623\u064a\u0636\u064b\u0627 \u062d\u062c\u0645 \u0627\u0644\u0646\u0645\u0648\u0630\u062c.<\/li>\n<li class=\"wp-block-list-item\"><code>min_S<\/code> \u0648 <code>max_S<\/code>: <strong>\u0646\u0637\u0627\u0642 \u0623\u0633\u0639\u0627\u0631 \u0627\u0644\u0623\u0633\u0647\u0645<\/strong> \u0627\u0644\u0630\u064a \u0646\u0631\u064a\u062f \u0623\u062e\u0630 \u0639\u064a\u0646\u0627\u062a \u0645\u0646\u0647 \u0639\u0646\u062f \u0625\u0646\u0634\u0627\u0621 \u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0635\u0637\u0646\u0627\u0639\u064a\u0629. \u0627\u0644\u062d\u062f \u0627\u0644\u0623\u062f\u0646\u0649 \u0648\u0627\u0644\u062d\u062f \u0627\u0644\u0623\u0642\u0635\u0649 \u0644\u0633\u0639\u0631 \u0627\u0644\u0633\u0647\u0645 \u0644\u062f\u064a\u0646\u0627.<\/li>\n<li class=\"wp-block-list-item\"><code>bias<\/code>: <strong>\u0625\u0632\u0627\u062d\u0629 \u0627\u062e\u062a\u064a\u0627\u0631\u064a\u0629 \u062a\u0636\u0627\u0641 \u0625\u0644\u0649 \u0623\u0633\u0639\u0627\u0631 \u0627\u0644\u062e\u064a\u0627\u0631\u0627\u062a<\/strong>\u060c \u0644\u0645\u062d\u0627\u0643\u0627\u0629 \u062a\u062d\u0648\u0644 \u0645\u0646\u0647\u062c\u064a \u0641\u064a \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a. \u064a\u062a\u0645 \u0630\u0644\u0643 \u0644\u0625\u0646\u0634\u0627\u0621 \u062a\u0628\u0627\u064a\u0646 \u0628\u064a\u0646 \u0627\u0644\u0639\u0627\u0644\u0645 \u0627\u0644\u062d\u0642\u064a\u0642\u064a \u0648\u0628\u064a\u0627\u0646\u0627\u062a Black-Scholes.<\/li>\n<li class=\"wp-block-list-item\"><code>noise_variance<\/code>: <strong>\u0645\u0642\u062f\u0627\u0631 \u0627\u0644\u0636\u0648\u0636\u0627\u0621<\/strong> \u0627\u0644\u0645\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0623\u0633\u0639\u0627\u0631 \u0627\u0644\u062e\u064a\u0627\u0631\u0627\u062a \u0644\u0645\u062d\u0627\u0643\u0627\u0629 \u0636\u0648\u0636\u0627\u0621 \u0627\u0644\u0642\u064a\u0627\u0633 \u0623\u0648 \u0627\u0644\u0633\u0648\u0642. \u062a\u062a\u0645 \u0625\u0636\u0627\u0641\u0629 \u0647\u0630\u0647 \u0627\u0644\u0645\u0639\u0644\u0645\u0629 \u0644\u0646\u0641\u0633 \u0627\u0644\u0633\u0628\u0628 \u0643\u0645\u0627 \u0643\u0627\u0646 \u0645\u0646 \u0642\u0628\u0644.<\/li>\n<li class=\"wp-block-list-item\"><code>epochs<\/code>: \u0639\u062f\u062f <strong>\u0627\u0644\u062a\u0643\u0631\u0627\u0631\u0627\u062a<\/strong> \u0627\u0644\u062a\u064a \u0633\u064a\u062a\u0645 \u062a\u062f\u0631\u064a\u0628 \u0627\u0644\u0646\u0645\u0648\u0630\u062c \u0639\u0644\u064a\u0647\u0627.<\/li>\n<li class=\"wp-block-list-item\"><code>lr<\/code>: <strong>\u0645\u0639\u062f\u0644 \u0627\u0644\u062a\u0639\u0644\u0645<\/strong> \u0644\u0644\u0645\u062d\u0633\u0646. \u064a\u062a\u062d\u0643\u0645 \u0647\u0630\u0627 \u0641\u064a \u0645\u062f\u0649 \u0633\u0631\u0639\u0629 \u062a\u062d\u062f\u064a\u062b \u0627\u0644\u0646\u0645\u0648\u0630\u062c \u0623\u062b\u0646\u0627\u0621 \u0627\u0644\u062a\u062f\u0631\u064a\u0628.<\/li>\n<li class=\"wp-block-list-item\"><code>log_interval<\/code>: \u0639\u062f\u062f \u0627\u0644\u0645\u0631\u0627\u062a (\u0645\u0646 \u062d\u064a\u062b \u0627\u0644\u0639\u0635\u0648\u0631) \u0627\u0644\u062a\u064a \u0646\u0631\u064a\u062f \u0641\u064a\u0647\u0627 <strong>\u0637\u0628\u0627\u0639\u0629 \u0627\u0644\u0633\u062c\u0644\u0627\u062a<\/strong> \u0644\u0645\u0631\u0627\u0642\u0628\u0629 \u062a\u0642\u062f\u0645 \u0627\u0644\u062a\u062f\u0631\u064a\u0628.<\/li>\n<\/ul>\n<p class=\"wp-block-paragraph\">\u062a\u0644\u0639\u0628 \u0643\u0644 \u0645\u0639\u0644\u0645\u0629 \u0645\u0646 \u0647\u0630\u0647 \u0627\u0644\u0645\u0639\u0644\u0645\u0627\u062a \u062f\u0648\u0631\u064b\u0627 \u0645\u062d\u062f\u062f\u064b\u0627\u060c \u062d\u064a\u062b \u064a\u0634\u0643\u0644 \u0628\u0639\u0636\u0647\u0627 \u0627\u0644\u0639\u0627\u0644\u0645 \u0627\u0644\u0645\u0627\u0644\u064a \u0627\u0644\u0630\u064a \u0646\u062d\u0627\u0643\u064a\u0647\u060c \u0628\u064a\u0646\u0645\u0627 \u064a\u062a\u062d\u0643\u0645 \u0627\u0644\u0628\u0639\u0636 \u0627\u0644\u0622\u062e\u0631 \u0641\u064a \u0643\u064a\u0641\u064a\u0629 \u062a\u0641\u0627\u0639\u0644 \u0634\u0628\u0643\u062a\u0646\u0627 \u0627\u0644\u0639\u0635\u0628\u064a\u0629 \u0645\u0639 \u0647\u0630\u0627 \u0627\u0644\u0639\u0627\u0644\u0645. \u064a\u0645\u0643\u0646 \u0623\u0646 \u062a\u0624\u062f\u064a \u0627\u0644\u062a\u0639\u062f\u064a\u0644\u0627\u062a \u0627\u0644\u0635\u063a\u064a\u0631\u0629 \u0647\u0646\u0627 \u0625\u0644\u0649 \u0633\u0644\u0648\u0643 \u0645\u062e\u062a\u0644\u0641 \u062a\u0645\u0627\u0645\u064b\u0627\u060c \u0645\u0645\u0627 \u064a\u062c\u0639\u0644 \u0647\u0630\u0627 \u0627\u0644\u0645\u0644\u0641 \u0642\u0648\u064a\u064b\u0627 \u0648\u062d\u0633\u0627\u0633\u064b\u0627. \u0633\u064a\u0624\u062f\u064a \u062a\u063a\u064a\u064a\u0631 \u0642\u064a\u0645 \u0645\u0644\u0641 JSON \u0647\u0630\u0627 \u0625\u0644\u0649 \u062a\u063a\u064a\u064a\u0631 \u062c\u0630\u0631\u064a \u0641\u064a \u0625\u062e\u0631\u0627\u062c \u0627\u0644\u0643\u0648\u062f.<\/p>\n<h3 class=\"wp-block-heading\">3.2 main.py (\u0645\u0644\u0641 main.py)<\/h3>\n<p class=\"wp-block-paragraph\">\u0627\u0644\u0622\u0646\u060c \u062f\u0639\u0648\u0646\u0627 \u0646\u0644\u0642\u064a \u0646\u0638\u0631\u0629 \u0639\u0644\u0649 \u0643\u064a\u0641\u064a\u0629 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0628\u0642\u064a\u0629 \u0627\u0644\u062a\u0639\u0644\u064a\u0645\u0627\u062a \u0627\u0644\u0628\u0631\u0645\u062c\u064a\u0629 \u0644\u0647\u0630\u0627 \u0627\u0644\u062a\u0643\u0648\u064a\u0646 \u0639\u0645\u0644\u064a\u064b\u0627.<\/p>\n<p class=\"wp-block-paragraph\">\u064a\u0623\u062a\u064a \u0627\u0644\u062c\u0632\u0621 \u0627\u0644\u0631\u0626\u064a\u0633\u064a \u0645\u0646 \u0627\u0644\u062a\u0639\u0644\u064a\u0645\u0627\u062a \u0627\u0644\u0628\u0631\u0645\u062c\u064a\u0629 \u0627\u0644\u062e\u0627\u0635\u0629 \u0628\u0646\u0627 \u0645\u0646 <strong><em>main.py<\/em><\/strong>\u060c \u0644\u062a\u062f\u0631\u064a\u0628 \u0634\u0628\u0643\u0629 PINN \u0627\u0644\u062e\u0627\u0635\u0629 \u0628\u0643 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 Torch\u060c \u0648 <strong><em>black_scholes<\/em>.py<\/strong>.<\/p>\n<p class=\"wp-block-paragraph\">\u0647\u0630\u0627 \u0647\u0648 \u0645\u0644\u0641 main.py:<\/p>\n<p class=\"wp-block-paragraph\">\u0625\u0630\u064b\u0627\u060c \u0645\u0627 \u064a\u0645\u0643\u0646\u0643 \u0641\u0639\u0644\u0647 \u0647\u0648:<\/p>\n<ol class=\"wp-block-list\">\n<li class=\"wp-block-list-item\">\u0625\u0646\u0634\u0627\u0621 \u0645\u0644\u0641 config.json \u0627\u0644\u062e\u0627\u0635 \u0628\u0643<\/li>\n<li class=\"wp-block-list-item\">\u062a\u0634\u063a\u064a\u0644 \u0627\u0644\u0623\u0645\u0631 <code>python main.py --config config.json<\/code><\/li>\n<\/ol>\n<p class=\"wp-block-paragraph\">\u064a\u0633\u062a\u062e\u062f\u0645 \u0645\u0644\u0641 main.py \u0627\u0644\u0643\u062b\u064a\u0631 \u0645\u0646 \u0627\u0644\u0645\u0644\u0641\u0627\u062a \u0627\u0644\u0623\u062e\u0631\u0649.<\/p>\n<h3 class=\"wp-block-heading\">3.3 black_scholes.py \u0648\u0627\u0644\u0645\u0633\u0627\u0639\u062f\u0627\u062a<\/h3>\n<p class=\"wp-block-paragraph\">\u064a\u0648\u062c\u062f \u062a\u0637\u0628\u064a\u0642 \u0646\u0645\u0648\u0630\u062c Black-Scholes \u062f\u0627\u062e\u0644 \u0627\u0644\u0645\u0644\u0641 <strong>black_scholes.py<\/strong>:<\/p>\n<p class=\"wp-block-paragraph\">\u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0647\u0630\u0627 \u0627\u0644\u0645\u0644\u0641 \u0644\u0628\u0646\u0627\u0621 \u0627\u0644\u0646\u0645\u0648\u0630\u062c \u0648\u062a\u062f\u0631\u064a\u0628\u0647 \u0648\u062a\u0635\u062f\u064a\u0631\u0647 \u0648\u0627\u0644\u062a\u0646\u0628\u0624 \u0628\u0647.<br \/>\n\u062a\u0633\u062a\u062e\u062f\u0645 \u0627\u0644\u062f\u0627\u0644\u0629 \u0628\u0639\u0636 \u0627\u0644\u0645\u0644\u0641\u0627\u062a \u0627\u0644\u0645\u0633\u0627\u0639\u062f\u0629 \u0623\u064a\u0636\u064b\u0627\u060c \u0645\u062b\u0644 data.py \u0648 loss.py \u0648 model.py.<br \/>\n\u064a\u0648\u062c\u062f \u0646\u0645\u0648\u0630\u062c Torch \u062f\u0627\u062e\u0644 \u0627\u0644\u0645\u0644\u0641 <strong>model.py<\/strong>:<\/p>\n<p class=\"wp-block-paragraph\">\u064a\u0648\u062c\u062f \u0645\u0646\u0634\u0626 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a (\u0628\u0627\u0644\u0646\u0638\u0631 \u0625\u0644\u0649 \u0645\u0644\u0641 \u0627\u0644\u062a\u0647\u064a\u0626\u0629) \u062f\u0627\u062e\u0644 \u0627\u0644\u0645\u0644\u0641 <strong>data.py<\/strong>:<\/p>\n<p class=\"wp-block-paragraph\">\u0648\u062f\u0627\u0644\u0629 \u0627\u0644\u062e\u0633\u0627\u0631\u0629 \u0627\u0644\u0645\u062f\u0645\u062c\u0629 \u0627\u0644\u062a\u064a \u062a\u062a\u0636\u0645\u0646 \u0642\u064a\u0645\u0629 \u0627\u0644\u0627\u0646\u062d\u0631\u0627\u0641 \u0647\u064a <strong>loss.py<\/strong>. \u0647\u0630\u0647 \u0627\u0644\u062f\u0627\u0644\u0629 \u0636\u0631\u0648\u0631\u064a\u0629 \u0644\u062a\u062d\u0633\u064a\u0646 \u062f\u0642\u0629 \u0627\u0644\u0646\u0645\u0648\u0630\u062c.<\/p>\n<h3 class=\"wp-block-heading\">4. \u0627\u0644\u0646\u062a\u0627\u0626\u062c<\/h3>\n<p class=\"wp-block-paragraph\">\u062d\u0633\u0646\u064b\u0627\u060c \u0639\u0646\u062f \u062a\u0634\u063a\u064a\u0644 main.py\u060c \u064a\u062a\u0645 \u062a\u062f\u0631\u064a\u0628 \u0634\u0628\u0643\u062a\u0646\u0627 \u0627\u0644\u0639\u0635\u0628\u064a\u0629 \u0627\u0644\u062a\u063a\u0630\u0648\u064a\u0629 \u0627\u0644\u0623\u0645\u0627\u0645\u064a\u0629 (FFNN)\u060c \u0648\u0646\u062d\u0635\u0644 \u0639\u0644\u0649 \u0645\u0627 \u064a\u0644\u064a:<\/p>\n<p><img decoding=\"async\" class=\"wp-image-601676 aligncenter\" src=\"https:\/\/www.dztecs.com\/ai\/wp-content\/uploads\/sites\/2\/2025\/05\/Screenshot-2025-04-16-at-6.40.02-PM-1024x201-1.png\" alt=\"\" \/ width=\"1024\" height=\"201\"><\/p>\n<p class=\"wp-block-paragraph\">\u0643\u0645\u0627 \u062a\u0644\u0627\u062d\u0638\u060c \u0641\u0625\u0646 \u062e\u0637\u0623 \u0627\u0644\u0646\u0645\u0648\u0630\u062c \u0644\u064a\u0633 \u062a\u0645\u0627\u0645\u064b\u0627 0\u060c \u0648\u0644\u0643\u0646 \u0645\u0639\u0627\u062f\u0644\u0629 PDE \u0644\u0644\u0646\u0645\u0648\u0630\u062c \u0623\u0635\u063a\u0631 \u0628\u0643\u062b\u064a\u0631 \u0645\u0646 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a. \u0647\u0630\u0627 \u064a\u0639\u0646\u064a \u0623\u0646 \u0627\u0644\u0646\u0645\u0648\u0630\u062c \u064a\u0642\u0648\u0645 (\u0628\u0634\u0643\u0644 \u0637\u0628\u064a\u0639\u064a) \u0628\u0641\u0631\u0636 \u062a\u0646\u0628\u0624\u0627\u062a\u0646\u0627 \u0628\u0642\u0648\u0629 \u0644\u062a\u0644\u0628\u064a\u0629 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u062a\u0641\u0627\u0636\u0644\u064a\u0629. \u0647\u0630\u0627 \u0628\u0627\u0644\u0636\u0628\u0637 \u0645\u0627 \u0642\u0644\u0646\u0627\u0647 \u0645\u0646 \u0642\u0628\u0644: \u0646\u062d\u0646 \u0646\u062d\u0633\u0646 \u0627\u0644\u0623\u062f\u0627\u0621 \u0645\u0646 \u062d\u064a\u062b \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0645\u062a\u0648\u0641\u0631\u0629 \u0644\u062f\u064a\u0646\u0627 \u0648\u0645\u0646 \u062d\u064a\u062b \u0646\u0645\u0648\u0630\u062c Black-Scholes.<\/p>\n<p class=\"wp-block-paragraph\">\u064a\u0645\u0643\u0646\u0646\u0627 \u0623\u0646 \u0646\u0644\u0627\u062d\u0638\u060c \u0646\u0648\u0639\u064a\u064b\u0627\u060c \u0648\u062c\u0648\u062f \u062a\u0637\u0627\u0628\u0642 \u0643\u0628\u064a\u0631 \u0628\u064a\u0646 \u0645\u062c\u0645\u0648\u0639\u0629 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0648\u0627\u0642\u0639\u064a\u0629 \u0627\u0644\u0645\u0634\u0648\u0634\u0629 + \u0627\u0644\u0645\u062a\u062d\u064a\u0632\u0629 (\u0648\u0627\u0642\u0639\u064a\u0629 \u0625\u0644\u0649 \u062d\u062f \u0645\u0627) \u0648\u0634\u0628\u0643\u0629 PINN.<\/p>\n<p><img decoding=\"async\" class=\"wp-image-601677 aligncenter\" src=\"https:\/\/www.dztecs.com\/ai\/wp-content\/uploads\/sites\/2\/2025\/05\/image-53.png\" alt=\"\" \/ width=\"989\" height=\"590\"><\/p>\n<p class=\"wp-block-paragraph\">\u0647\u0630\u0647 \u0647\u064a \u0627\u0644\u0646\u062a\u0627\u0626\u062c \u0639\u0646\u062f\u0645\u0627 \u062a\u0643\u0648\u0646 t = 0\u060c \u0648\u064a\u062a\u063a\u064a\u0631 \u0633\u0639\u0631 \u0627\u0644\u0633\u0647\u0645 \u0645\u0639 \u062e\u064a\u0627\u0631 \u0627\u0644\u0634\u0631\u0627\u0621 \u0639\u0646\u062f \u0642\u064a\u0645\u0629 t \u062b\u0627\u0628\u062a\u0629. \u0631\u0627\u0626\u0639 \u062c\u062f\u064b\u0627\u060c \u0623\u0644\u064a\u0633 \u0643\u0630\u0644\u0643\u061f \u0648\u0644\u0643\u0646 \u0627\u0644\u0623\u0645\u0631 \u0644\u0645 \u064a\u0646\u062a\u0647 \u0628\u0639\u062f! \u064a\u0645\u0643\u0646\u0643 \u0627\u0633\u062a\u0643\u0634\u0627\u0641 \u0627\u0644\u0646\u062a\u0627\u0626\u062c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0643\u0648\u062f \u0623\u0639\u0644\u0627\u0647 \u0628\u0637\u0631\u064a\u0642\u062a\u064a\u0646:<\/p>\n<ol class=\"wp-block-list\">\n<li class=\"wp-block-list-item\">\u0627\u0644\u0644\u0639\u0628 \u0628\u0627\u0644\u0639\u062f\u064a\u062f \u0645\u0646 <strong>\u0627\u0644\u0645\u0639\u0644\u0645\u0627\u062a (parameters)<\/strong> \u0627\u0644\u0645\u0648\u062c\u0648\u062f\u0629 \u0641\u064a config.json<\/li>\n<li class=\"wp-block-list-item\">\u0631\u0624\u064a\u0629 \u0627\u0644\u062a\u0646\u0628\u0624\u0627\u062a \u0639\u0646\u062f <strong>t&gt;0<\/strong><\/li>\n<\/ol>\n<p class=\"wp-block-paragraph\">\u0627\u0633\u062a\u0645\u062a\u0639! \ud83d\ude42<\/p>\n<h3 class=\"wp-block-heading\">5. \u0627\u0633\u062a\u0646\u062a\u0627\u062c\u0627\u062a<\/h3>\n<p class=\"wp-block-paragraph\">\u0634\u0643\u0631\u0627\u064b \u062c\u0632\u064a\u0644\u0627\u064b \u0644\u0648\u0635\u0648\u0644\u0643\u0645 \u0625\u0644\u0649 \u0647\u0646\u0627. \u062d\u0642\u0627\u064b\u060c \u0643\u0627\u0646\u062a \u0647\u0630\u0647 \u0631\u062d\u0644\u0629 \u0637\u0648\u064a\u0644\u0629 \ud83d\ude05<br \/>\n\u0625\u0644\u064a\u0643\u0645 \u0645\u0627 \u0627\u0633\u062a\u0639\u0631\u0636\u0646\u0627\u0647 \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0645\u0642\u0627\u0644\u0629:<\/p>\n<ol class=\"wp-block-list\">\n<li class=\"wp-block-list-item\"><strong>\u0628\u062f\u0623\u0646\u0627 \u0628\u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621<\/strong>\u060c \u0648\u0643\u064a\u0641 \u0623\u0646 \u0642\u0648\u0627\u0646\u064a\u0646\u0647\u0627\u060c \u0627\u0644\u0645\u0643\u062a\u0648\u0628\u0629 \u0643\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062a\u0641\u0627\u0636\u0644\u064a\u0629\u060c \u0639\u0627\u062f\u0644\u0629\u060c \u0648\u062c\u0645\u064a\u0644\u0629\u060c \u0648\u0642\u0627\u0628\u0644\u0629 \u0644\u0644\u062a\u0646\u0628\u0624 (\u0639\u0627\u062f\u0629\u064b).<\/li>\n<li class=\"wp-block-list-item\"><strong>\u0627\u0646\u062a\u0642\u0644\u0646\u0627 \u0625\u0644\u0649 \u0627\u0644\u062a\u0645\u0648\u064a\u0644<\/strong>\u060c \u0648\u0627\u0644\u062a\u0642\u064a\u0646\u0627 \u0628\u0646\u0645\u0648\u0630\u062c \u0628\u0644\u0627\u0643-\u0634\u0648\u0644\u0632 Black-Scholes Model\u2014 \u0648\u0647\u064a \u0645\u0639\u0627\u062f\u0644\u0629 \u062a\u0641\u0627\u0636\u0644\u064a\u0629 \u062a\u0647\u062f\u0641 \u0625\u0644\u0649 \u062a\u0633\u0639\u064a\u0631 \u0627\u0644\u062e\u064a\u0627\u0631\u0627\u062a \u0628\u0637\u0631\u064a\u0642\u0629 \u062e\u0627\u0644\u064a\u0629 \u0645\u0646 \u0627\u0644\u0645\u062e\u0627\u0637\u0631.<\/li>\n<li class=\"wp-block-list-item\"><strong>\u0627\u0633\u062a\u0643\u0634\u0641\u0646\u0627 \u0627\u0644\u0634\u0628\u0643\u0627\u062a \u0627\u0644\u0639\u0635\u0628\u064a\u0629 \u0627\u0644\u0645\u0633\u062a\u0646\u064a\u0631\u0629 \u0628\u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621 (PINNs)<\/strong>\u060c \u0648\u0647\u064a \u0646\u0648\u0639 \u0645\u0646 \u0627\u0644\u0634\u0628\u0643\u0627\u062a \u0627\u0644\u0639\u0635\u0628\u064a\u0629 \u0644\u0627 \u062a\u0643\u062a\u0641\u064a \u0628\u0645\u0637\u0627\u0628\u0642\u0629 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0648\u0644\u0643\u0646\u0647\u0627 \u062a\u062d\u062a\u0631\u0645 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u062a\u0641\u0627\u0636\u0644\u064a\u0629 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629. \u062a\u0639\u062a\u0628\u0631 PINNs \u0623\u062f\u0627\u0629 \u0642\u0648\u064a\u0629 \u0641\u064a \u0646\u0645\u0630\u062c\u0629 \u0627\u0644\u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u0645\u0639\u0642\u062f\u0629.<\/li>\n<li class=\"wp-block-list-item\"><strong>\u0646\u0641\u0630\u0646\u0627 \u0643\u0644 \u0634\u064a\u0621 \u0641\u064a Python Python<\/strong>\u060c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 PyTorch \u0648\u0642\u0627\u0639\u062f\u0629 \u0628\u064a\u0627\u0646\u0627\u062a \u0645\u0639\u064a\u0627\u0631\u064a\u0629 \u0646\u0638\u064a\u0641\u0629 \u062a\u062a\u064a\u062d \u0644\u0643 \u062a\u0639\u062f\u064a\u0644 \u0627\u0644\u0645\u0639\u0644\u0645\u0627\u062a\u060c \u0648\u0625\u0646\u0634\u0627\u0621 \u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0635\u0637\u0646\u0627\u0639\u064a\u0629\u060c \u0648\u062a\u062f\u0631\u064a\u0628 \u0634\u0628\u0643\u0627\u062a PINNs \u0627\u0644\u062e\u0627\u0635\u0629 \u0628\u0643 \u0644\u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0629 \u0628\u0644\u0627\u0643-\u0634\u0648\u0644\u0632 Black-Scholes.<\/li>\n<li class=\"wp-block-list-item\"><strong>\u0635\u0648\u0631\u0646\u0627 \u0627\u0644\u0646\u062a\u0627\u0626\u062c<\/strong> \u0648\u0631\u0623\u064a\u0646\u0627 \u0643\u064a\u0641 \u062a\u0639\u0644\u0645\u062a \u0627\u0644\u0634\u0628\u0643\u0629 \u0623\u0646 \u062a\u0637\u0627\u0628\u0642 \u0644\u064a\u0633 \u0641\u0642\u0637 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0645\u0634\u0648\u0634\u0629 \u0648\u0644\u0643\u0646 \u0623\u064a\u0636\u0627\u064b \u0627\u0644\u0633\u0644\u0648\u0643 \u0627\u0644\u0645\u062a\u0648\u0642\u0639 \u0645\u0646 \u0645\u0639\u0627\u062f\u0644\u0629 \u0628\u0644\u0627\u0643-\u0634\u0648\u0644\u0632 Black-Scholes.<\/li>\n<\/ol>\n<p class=\"wp-block-paragraph\">\u0623\u0639\u0644\u0645 \u0623\u0646 \u0627\u0633\u062a\u064a\u0639\u0627\u0628 \u0643\u0644 \u0647\u0630\u0627 \u062f\u0641\u0639\u0629 \u0648\u0627\u062d\u062f\u0629 \u0644\u064a\u0633 \u0628\u0627\u0644\u0623\u0645\u0631 \u0627\u0644\u0633\u0647\u0644. \u0641\u064a \u0628\u0639\u0636 \u0627\u0644\u0645\u062c\u0627\u0644\u0627\u062a\u060c \u0643\u0646\u062a \u0645\u0642\u062a\u0636\u0628\u0627\u064b \u0628\u0627\u0644\u0636\u0631\u0648\u0631\u0629\u060c \u0631\u0628\u0645\u0627 \u0623\u0642\u0635\u0631 \u0645\u0645\u0627 \u0643\u0646\u062a \u0628\u062d\u0627\u062c\u0629 \u0625\u0644\u064a\u0647. \u0648\u0645\u0639 \u0630\u0644\u0643\u060c \u0625\u0630\u0627 \u0643\u0646\u062a \u062a\u0631\u063a\u0628 \u0641\u064a \u0631\u0624\u064a\u0629 \u0627\u0644\u0623\u0645\u0648\u0631 \u0628\u0637\u0631\u064a\u0642\u0629 \u0623\u0643\u062b\u0631 \u0648\u0636\u0648\u062d\u0627\u064b\u060c \u0645\u0631\u0629 \u0623\u062e\u0631\u0649\u060c \u0623\u0644\u0642\u0650 \u0646\u0638\u0631\u0629 \u0639\u0644\u0649 <a target=\"_blank\" rel=\"noopener noreferrer\" href=\"https:\/\/github.com\/PieroPaialungaAI\/BlackScholesPINN\/tree\/main\">\u0645\u062c\u0644\u062f GitHub.<\/a> \u062d\u062a\u0649 \u0625\u0630\u0627 \u0644\u0645 \u062a\u0643\u0646 \u0645\u0647\u062a\u0645\u0627\u064b \u0628\u0627\u0644\u0628\u0631\u0627\u0645\u062c\u060c \u0641\u0647\u0646\u0627\u0643 \u0645\u0644\u0641 README.md \u0648\u0627\u0636\u062d \u0648\u0646\u0645\u0648\u0630\u062c \u0628\u0633\u064a\u0637 <strong>example\/BlackScholesModel.ipynb<\/strong> \u064a\u0634\u0631\u062d \u0627\u0644\u0645\u0634\u0631\u0648\u0639 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629.<\/p>\n<p>&nbsp;<\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"<p>\u0625\u062e\u0644\u0627\u0621 \u0645\u0633\u0624\u0648\u0644\u064a\u0629: \u0647\u0630\u0647 \u0644\u064a\u0633\u062a \u0646\u0635\u064a\u062d\u0629 \u0645\u0627\u0644\u064a\u0629. \u0623\u0646\u0627 \u062d\u0627\u0635\u0644 \u0639\u0644\u0649 \u062f\u0631\u062c\u0629 \u0627\u0644\u062f\u0643\u062a\u0648\u0631\u0627\u0647 \u0641\u064a \u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u0637\u064a\u0631\u0627\u0646 \u0645\u0639 \u062a\u0631\u0643\u064a\u0632 \u0642\u0648\u064a \u0639\u0644\u0649 \u062a\u0639\u0644\u0645 \u0627\u0644\u0622\u0644\u0629: \u0623\u0646\u0627 \u0644\u0633\u062a \u0645\u0633\u062a\u0634\u0627\u0631\u064b\u0627 \u0645\u0627\u0644\u064a\u064b\u0627. \u0647\u0630\u0647 \u0627\u0644\u0645\u0642\u0627\u0644\u0629 \u0645\u062e\u0635\u0635\u0629 \u0641\u0642\u0637 \u0644\u0625\u0638\u0647\u0627\u0631 \u0642\u0648\u0629 \u0627\u0644\u0634\u0628\u0643\u0627\u062a \u0627\u0644\u0639\u0635\u0628\u064a\u0629 \u0627\u0644\u0645\u0633\u062a\u0646\u064a\u0631\u0629 \u0628\u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621 (PINNs) \u0641\u064a \u0633\u064a\u0627\u0642 \u0645\u0627\u0644\u064a. \u0639\u0646\u062f\u0645\u0627 \u0643\u0627\u0646 \u0639\u0645\u0631\u064a 16 \u0639\u0627\u0645\u064b\u0627\u060c \u0648\u0642\u0639\u062a \u0641\u064a \u062d\u0628 \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621. \u0643\u0627\u0646 \u0627\u0644\u0633\u0628\u0628 \u0628\u0633\u064a\u0637\u064b\u0627 \u0648\u0644\u0643\u0646\u0647 \u0642\u0648\u064a: \u0627\u0639\u062a\u0642\u062f\u062a \u0623\u0646 \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621 [&hellip;]<\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"author":3,"featured_media":3633,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[14],"tags":[],"class_list":["post-3632","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-ai"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.6 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u0639\u0646\u062f\u0645\u0627 \u064a\u0644\u062a\u0642\u064a \u0639\u0644\u0645 \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621 \u0628\u0627\u0644\u062a\u0645\u0648\u064a\u0644: \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0630\u0643\u0627\u0621 \u0627\u0644\u0627\u0635\u0637\u0646\u0627\u0639\u064a \u0644\u062d\u0644 \u0645\u0639\u0627\u062f\u0644\u0629 \u0628\u0644\u0627\u0643-\u0634\u0648\u0644\u0632<\/title>\n<meta name=\"description\" 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